4. Additional cabinet info - The exterior and interior of the cabinets look correctly done with the tapered beech wood battens (support braces). Examine the interior foam carefully. It is actually unusual for it to be a nice whitish yellow color, indicating new or completely sealed and unmolested. More commonly, there is, for a 45 year old speaker, some darker yellowing along the edges, particularly in front. Some speakers were damaged by being overdriven, would show some scorching or burning along sides next to the resistors on the left side of the crossover. Lift the edges of the foam pieces and see if there is any date stamp on the inner cabinet walls or battens. The Greaves sticker is usually not seen but under the foam insulation if present, so should not be anywhere near the baffle seal. It should be moved back to under the bottom foam. There should also be thin bituminous damping pads on the back wall and sides, and top/bottom. These help to control cabinet resonances while the foam absorbs standing waves. I noticed a couple of the screw holes in the battens appear to have been screwed into twice and not in the same place, suggesting the screw was replaced and screwed in off axis from the original hole, or the baffle was mounted upside down and did not align correctly. I don't see any evidence of the thin inner baffle gasket that should interface between the battens and baffle board, sealing the baffle. That should be reviewed and sourced.
5. Baffle board - Most but not all Rogers had serial numbers written on the back inside bottom of the board below the woofer. The board should be a 9 ply baltic birch plywood. It should look slightly crude because it was cut with rough machinery back then, not precision CNC stuff like today. It is possible someone had replaced the baffle board in the past if these identifiers don't show here or you just didn't get one that had it written on.
6. Drivers - Woofers - On the one woofer that you show (and mentioned that both are KEF Constructor versions), I'm sad but not surprised to say these are replacements for the original, selected, KEF B110 SP1003, circa 1975-77. Todd's pic shows the front of the SP1003 showing the bextrene cone with front outer painted on plastiflex PVA damping coating and thicker, short inner attachment Neoprene surround, black chassis, and narrow rectangular ID label with SP1003 and usually another with a cryptic date code. A glimpse of yours clearly shows the B110B SP1057 designation, a later midwoofer designed and used in the KEF R101 and as a midrange for the KEF 105 series and a few other floor standers. This woofer is identified by the smooth rounded magnet pole piece/back, the smooth bare bextrene front (coating now on the back) and slightly flattened and wider inner attachment PVC roll surround - it is a bit more compliant. The SP1057 has different frequency and Thiele/Small characteristics compared to the original SP1003, and also benefits from newer voice coil adhesives and materials. A lot of LS3/5a's have had their woofers replaced like this because folks did not realize the difference, or felt buyers would not know the difference either. The woofer appears to have the correct, possibly reused PVC channel gasket around the frame edge to decouple it from the baffle. The bolts and nuts and felt washers appear correct.
This is not to say the speakers wouldn't sound good, or even a bit similar. However, the crossover is specifically designed for the SP1003 and using the SP1057 is not going to adhere nor give the correct BBC LS3/5a specific frequency response. It can sound good, even pretty good, but not accurately correct. The Constructor series versions, as mentioned above, were outliers or non-matches when produced, and not used in KEF's stringent computer grading and selection process of the day. KEF put them to DIY market use where builders did not necessarily have ways to get down to the nth +/- 0.5db adherence to spec, so had pleasant sounding speakers with the character of if not the exact frequency response of DIY designs prevalent of the era.
The good thing is both speakers, if having the same SP1057, will sound reasonably matched in character. If one was SP1003 and the other SP1057, there probably would be some deviation that you could more readily hear.
7. Drivers - Tweeters. Sad to see one of your original tweeters was poked in. Was the perforated cover missing from it? Does the date code on the side or back of the original tweeter reasonably match the other tweeter that has the cover? IF so, you may want to try to salvage the dented tweeter just for fun, assuming it still has continuity across its terminals when check for DC resistance. To pull it out, you need to wipe the faceplate clean with a moist cloth. Avoid any solvents. Dry your mouth and place rounded and pursed lips over the entire tweeter circumference, creating a seal. Then gently but firmly create vacuum with your cheeks and tongue - trying to suck out the dome. You will have to vary the suction and see what happens or works. If you are persistent and a bit lucky, the dome will pop back up and out. However, its likely there will be a couple of dimples on the dome which are hard to fully remove. It will be unknown if it works properly till you test the tweeter with a HF signal (3K and higher) and low power amp, preferably with a blocking cap. The voice coil can get canted or tilted unless the roll surround looks even height all around. You can also use a vacuum wand from a vacuum cleaner that can seal around the entire tweeter dome but it must have some way to crudely adjust the vacuum AND be easy to hold in place. You may need some help by someone else turning the vacuum on and off while you manipulate the hose or attachment. Avoid brushes for obvious reasons.
That said, replacing the T27's is not uncommon and I'm unaware that they varied too much in frequency response or were selected to any degree. If upon listening they sound pretty symmetrically similar in quality and HF loudness and timbre, I'd leave well enough alone. OTOH, if the T27's came as a pair from a pair of KEF speakers, they might be more matched to each other (particularly if their date codes are similar) than one old and one "new used". Your ears or test instrumentation would be able to tell better.
There should be a very thin circular foam gasket under the tweeter to seal against the baffle. On the back of the tweeter should be a 1/4" thick square felt pad that helps to damp the crossover when mounted behind the tweeter on the 4 standoffs. The tweeters should be mounted so that the visible wires are horizontal. The perforated protection grille should be in placed and glued down to the tweeter as it assists the HF response. The 4 outer felt damping strips that form a dam around the tweeter prevent cabinet and grille edge diffraction. Yours appear original, as does the (sometimes poorly) stapled velcro baffle strips.
8. Grilles - your grilles appear to be the correct woven Tygan grilles. They have the slightly later short rectangular silver letter on black background badges. Earlier units had bronze metal badges. I think yours are correct. One grille appears to have a fabric pull tab, can't tell about the other. This help getting the grille off of the velcro mounting which is pretty firm or tight. In the future, if you need to pull the grilles and don't have the tab, insert a thick plastic credit card and use it to gently pry top or bottom out till you can get the grille started. Most grilles were made from a plywood or later MDF frame.